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Introductory & Intermediate Algebra for College Students

Introductory & Intermediate Algebra for College Students

Summary

The goal of this series is to provide readers with a strong foundation in Algebra. Each book is designed to develop readers' critical thinking and problem-solving capabilities and prepare readers for subsequent Algebra courses as well as service math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving. The Real Number System. Linear Equations and Inequalities in One Variable. Linear Equations in Two Variables. Systems of Linear Equations. Exponents and Polynomials. Factoring Polynomials. Rational Expressions. Functions, More on Systems of Linear Functions. Inequalities and Problem Solving. Radicals, Radical Functions, and Rational Exponents. Quadratic Equations and Functions. Exponential and Logarithmic Functions. Conic Sections and Nonlinear Systems of Equations. Sequences, Induction, and Probability. For anyone interested in introductory and intermediate algebra and for the combined introductory and intermediate algebra.

Table of Contents

Preface

xi

To the Student

xvii

About the Author

xix

Applications Index

xxv

The Real Number System

3

(98)

Fractions

4

(10)

The Real Numbers

14

(11)

Ordered Pairs and Graphs

25

(10)

Basic Rules of Algebra

35

(12)

Addition of Real Numbers

47

(8)

Subtraction of Real Numbers

55

(8)

Multiplication and Division of Real Numbers

63

(12)

Exponents, Order of Operations, and Mathematical Models

75

(26)

Chapter 1 Group Projects

80

(10)

Summary

90

(4)

Review Exercises

94

(3)

Chapter 1 Test

97

(4)

Linear Equations and Inequalities in one variable

101

(84)

The Addition Property of Equality

102

(8)

The Multiplication Property of Equality

110

(8)

Solving Linear Equations

118

(8)

Formulas and Percents

126

(9)

An Introduction to Problem Solving

135

(12)

Problem Solving in Geometry

147

(12)

Solving Linear Inequalities

159

(26)

Chapter 2 Group Projects

172

(1)

Summary

173

(5)

Review Exercises

178

(3)

Chapter 2 Test

181

(1)

Cumulative Review Exercises (Chapters 1--2)

182

(3)

Linear Equations in Two Variables

185

(60)

Graphing Linear Equations

186

(12)

Graphing Linear Equations Using Intercepts

198

(10)

Slope

208

(9)

The Slope-Intercept Form of the Equation of a Line

217

(8)

The Point-Slope Form of the Equation of a Line

225

(20)

Chapter 3 Group Projects

235

(1)

Summary

236

(3)

Review Exercises

239

(3)

Chapter 3 Test

242

(1)

Cumulative Review Exercises (Chapters 1--3)

243

(2)

Systems of Linear Equations

245

(50)

Solving Systems of Linear Equations by Graphing

246

(9)

Solving Systems of Linear Equations by the Substitution Method

255

(7)

Solving Systems of Linear Equations by the Addition Method

262

(9)

Problem Solving Using Systems of Equations

271

(24)

Chapter 4 Group Projects

286

(1)

Summary

287

(2)

Review Exercises

289

(2)

Chapter 4 Test

291

(1)

Cumulative Review Exercises (Chapters 1--4)

292

(3)

Exponents and Polynomials

295

(78)

Adding and Substracting Polynomials

296

(8)

Multiplying Polynomials

304

(11)

Special Products

315

(9)

Polynomials in Several Variables

324

(8)

Dividing Polynomials

332

(8)

Dividing Polynomials by Binomials; Synthetic Division

340

(11)

Negative Exponents and Scientific Notation

351

(22)

Chapter 5 Group Projects

3363

Summary

364

(3)

Review Exercises

367

(3)

Chapter 5 Test

370

(1)

Cumulative Review Exercises (Chapters 1--5)

370

(3)

Factoring Polynomials

373

(58)

The Greatest Common Factor and Factoring by Grouping

374

(8)

Factoring Trinomials Whose Leading Coefficient Is One

382

(7)

Factoring Trinomials Whose Leading Coefficient Is Not One

389

(7)

Factoring Special Forms

396

(7)

A General Factoring Strategy

403

(8)

Solving Quadratic Equations by Factoring

411

(20)

Chapter 6 Group Projects

423

(1)

Summary

424

(2)

Review Exercises

426

(2)

Chapter 6 Test

428

(1)

Cumulative Review Exercises (Chapters 1--6)

428

(3)

Rational Expressions

431

(86)

Rational Expressions and Their Simplification

432

(9)

Multiplying and Dividing Rational Expressions

441

(7)

Adding and Subtracting Rational Expressions with the Same Denominators

448

(8)

Adding and Substracting Rational Expressions with Different Denominators